# Problems on Trains Questions

FACTS  AND  FORMULAE  FOR  PROBLEMS  ON  TRAINS

1. a km/hr = [a x (5/18)] m/s.

2. a m/s = [a x (18/5)] km/hr.

3. Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.

4. Time taken by a train of length 1 metres to pass a stationary object of length b metres is the time taken by the train to cover (1 + b) metres.

5. Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relatives speed = (u - v) m/s.

6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed = (u + v) m/s.

7. If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other = $\frac{\left(a+b\right)}{\left(u+v\right)}$sec.

8. If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then the time taken by the faster train to cross the slower train = $\frac{\left(a+b\right)}{\left(u-v\right)}$sec.

9. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A's speed) : (B’s speed) = $\left(\sqrt{b}:\sqrt{a}\right)$

Q:

A train travelling at the speed of 66 kmph crosses a 300 m long platform in 24 seconds. How long was the train?

 A) 140 m B) 240 m C) 160 m D) 180 m

Explanation:

2 860
Q:

A train starts from a place A at 8:00 a.m. and arrives at another place B at 1:30 p.m. on the same day. If the speed of the train is 30 km/hr, then what will be the distance (in km) covered by the train?

 A) 165 B) 175 C) 150 D) 135

Explanation:

4 857
Q:

Two trains are running in opposite direction with the same speed. If the length of each train is 80 metres and they cross each other in 16 seconds, then what is the speed (in km/hr) of each train?

 A) 12 B) 18 C) 24 D) 30

Explanation:

0 843
Q:

A train runs at 80 kmph for the first 40 km and the next 30 km at 60 kmph. Find the average speed.

 A) 62 kmph B) 64 kmph C) 65 kmph D) 70 kmph

Explanation:

2 832
Q:

A superfast Duronto express running at 90 kmph overtakes a bike running at 36 kmph in 25 seconds. What is the length of the train in meters?

 A) 375 m B) 225 m C) 275 m D) 325 m

Explanation:

2 816
Q:

A train having a length of 500 m through a tunnel of 1000 m in 1 minute. What is the speed of the train in km/hr ?

 A) 75 km/hr B) 90 km/hr C) 87 km/hr D) 96 km/hr

Explanation:

2 802
Q:

A train moving with a uniform speed covers 338 m in 50 s. What is its speed?

 A) 5.76 m/s B) 7.76 m/s C) 6.76 m/s D) 4.76 m/s

Explanation:

0 795
Q:

A man misses a train by 1 hour if he travels at a speed of 4 kmph. If he had increased his speed to 5 kmph, he would gave still missed the train by 24 minutes. At what speed should he have travelled so that he reached the station exactly on time?

 A) 12 kmph B) 6 kmph C) 10 kmph D) 8 kmph